Bike wheels and their different sizes

There is hardly any part of the bike which influences the riding behaviour as strongly as the wheels do. The weight which can be saved at the rotating mass is clearly noticeable, and also the stiffness of the wheels contributes considerably to the handling and thus to the fun in riding.
Meanwhile you'll find system wheels everywhere, meaning that all the parts (hub, spokes, nipples, rims) are from one manufacturer and coordinated to each other. But traditional wheels with a classic lacing pattern or wheel sets put together according to one's own wishes are still strongly represented.

Depending on the type of bike sport, there are different sizes.

Overview of the MTB wheels

In the MTB sector, 29 & 27.5" wheels are mainly used for new bikes. The formerly mostly used 26" wheels are meanwhile being used more and more seldom on the mountain bike, except if the bikes in question are DH/FR bikes or also fat bikes.
When changing the wheel, you do not only have to observe the wheel size but also the hub width and the axle standard. There have been al lot of new developments within the last years in that regard.
Also important is which drivetrain you wish to use. Whoever wants to use 8/9/10-fold Shimano or Sram, will manage with the "regular" freewheel. Even 11 speed Shimano MTB is possible with the normal freewheel. But if you decide to use 11 speed Sram, you will need an XD-freewheel with which you can also use the new E 13 10/11 speed cassettes. There is so much to be observed!

The decision for a wheel also includes the question which brake is going to be used: One still distinguishes between wheels for rim brakes and disc wheels (thus for the combination with disc brakes).
Disc brakes are almost standard in the MTB field, but the fitting mount for the disc must still be observed, namely 6-hole IS 2000 or CenterLock. Depending on the desired tire width and application purpose, differently wide and sturdy rims are being used. The rim of the road bike is especially narrow. Downhill rims in contrast are not only wider but also score with especially good sturdiness, which is vital for their application.

Overview of the road bike wheels

Road bike wheels and thriathlon wheels are primarily found in 28". Sporadically, there are still 26" models for young people or women. In the triathlon sector, there used to be 26" wheels, but they have meanwhile been done away with. As to the freewheel, road bikers with Campagnolo drivetrains also must observe a special freewheel. Same as in the MTB segment, hydraulic disc brakes meanwhile are gaining entry into the road bike segment.
If the decision is made to either use disc or rim brake wheels, the road biker then has wheels for tubular tires or clinchers at his disposal.
Since the weight and the sturdiness of the wheels are very important to the usual road biker, there are more and more light carbon wheels with aerodynamic shape and blade spokes in use in the high-price segment.

Almost all of the trekking bikes roll on 28", but in general with wider rims than the road bikes have. Depending on the price, the braking still occurs on the rim or with a disc. Widely spread are also hub dynamos on the front wheel.

Truing the wheel, what does it mean?

All wheels should be checked from time to time. Important is not only to observe lateral or vertical runouts, but also the spoke tension. Whoever controls the tension and lets the wheels be trued, if required (if you do not do it yourself), can thus prevent costly repairs or rim & spoke exchanges. The simple control is really very simple: you just turn your bike over if you do not have a bike holder. Then, you take two spokes which are closest to each other from one side between thumb & index finger and slightly press them together. Now you do that on both sides, best is to start by the valve and to go once all around. If you cannot feel any difference in the tension, it is already a good sign. Even slight lateral or vertical runouts do not necessarily mean that the rim must be exchanged, often you can do the truing yourself with the right tool and some knowledge. However, it takes a little practice, since if you only pay attention to lateral runouts, you can catch some undesired and clearly difficult centrable vertical runouts.
PS: Whoever wants to exactly determine the spoke tension, should place emphasis on a socalled tensiometer.